One common scenario is after a major fight between them. Naruto might feel that the relationship has become too strained and decides to avoid Sasuke to give both of them time to cool down. For instance, if they had a very intense battle over different ideologies and Naruto realizes that they can't immediately reconcile, he would avoid Sasuke.
In some fanfictions, external forces could be at play. For example, a powerful villain might be manipulating the situation to drive a wedge between Naruto and Sasuke. The villain could spread false information or create situations that make Naruto believe he should avoid Sasuke for the safety of himself or others. This often leads to a complex web of events where Naruto has to figure out the truth while trying to deal with his feelings of avoiding Sasuke.
Sometimes, it could be because of a love triangle situation in the fanfiction. If there is a character who has feelings for both Naruto and Sasuke, Naruto might avoid Sasuke to avoid the awkwardness and potential conflict that could arise from this situation. He may think that by keeping his distance, he can let things sort themselves out.
A common scenario is when Naruto is given a special mission or task that Sasuke feels he should have been chosen for. Sasuke's pride and his competitive nature with Naruto make him jealous. He might think that Naruto is being favored over him.
A common scenario is Naruto using his friendship - power. His bond with his friends gives him extra strength, and he uses this emotional power to overpower Sasuke. Another is that Naruto discovers a new power within himself during the fight, like a hidden form of the Nine - Tails' chakra.
One common scenario is during training sessions. Naruto's enthusiasm, Sasuke's determination, and Sakura's focus combine well. They push each other to improve their skills. Another is when they are on a mission together. Naruto might crack jokes to lighten the mood, Sasuke stays focused on the mission goals, and Sakura uses her medical skills and strategic thinking to keep them all in good shape. They learn to trust each other more in these situations.
One common scenario is that they get trapped in a different dimension together. In this strange new place, they have to rely on each other to survive. Without the distractions of their normal lives and the expectations of the village, they really get to know each other on a deeper level and become best friends.
One common scenario is when Naruto gets injured during a mission. Sasuke, being the one to take care of him, uses his skills to heal Naruto or at least keep him stable until proper medical help arrives. Another scenario could be Sasuke protecting Sakura from an enemy's attack, perhaps even sacrificing himself a bit in the process. And sometimes, Sasuke might help Sakura in her medical research, providing her with rare herbs or knowledge he's acquired during his travels.
One common scenario is when they are facing a powerful enemy. Sasuke would put herself in harm's way to protect Naruto. Another scenario could be when Naruto is in an emotional distress. Sasuke would be there to comfort and protect him from any further harm. For example, if Naruto is feeling down because of the villagers' attitude towards him, Sasuke would stand up for him and make sure no one takes advantage of his vulnerable state.
One possible scenario could be a power imbalance. Maybe Sasuke discovers some new, extremely powerful jutsu that Naruto has no defense against. For example, a jutsu that can nullify Naruto's chakra or attack his spirit directly. Another possibility is a miscommunication or a breakdown in their relationship. If Sasuke believes Naruto has betrayed him in some way, his anger could lead him to kill Naruto. However, this goes against the core of their bond in the original series.
One possible scenario could be that they sacrifice themselves to save the village from an ultimate evil. They might combine their powers in a final, desperate move that exhausts them completely, leading to their deaths.
One possible scenario could be that Naruto snaps at Sasuke over his constant pursuit of power at the expense of their friendship. Maybe Sasuke makes a decision to leave the village again for more power, and Naruto, tired of his friend's self - destructive ways, snaps and tries to make him see reason.
One interesting scenario could be a fight in an alternate dimension where the rules of chakra are different. This would force both Naruto and Sasuke to adapt new strategies. Another could be a battle where they are forced to team up against a common enemy first before their duel, which would add a complex layer of emotions and dynamics.